Journal of Experimental Psychology: Human Perception and Performance 2006, Vol. 32, No. 5, 1266 –1275

Copyright 2006 by the American Psychological Association 0096-1523/06/$12.00 DOI: 10.1037/0096-1523.32.5.1266

Haptic Tracking Permits Bimanual Independence David A. Rosenbaum, Amanda M. Dawson, and John H. Challis Pennsylvania State University This study shows that in a novel task— bimanual haptic tracking—neurologically normal human adults can move their 2 hands independently for extended periods of time with little or no training. Participants lightly touched buttons whose positions were moved either quasi-randomly in the horizontal plane by 1 or 2 human drivers (Experiment 1), in circle and square patterns in the vertical plane by 2 human drivers (Experiment 2), or at different frequencies in the horizontal plane by 2 human drivers (Experiment 3). Bimanual contact was maintained equally well in all conditions even though in Experiment 1 the left- and right-hand motions were uncorrelated (in the 2-driver condition), in Experiment 2 the left- and right-hand motions were spatially incongruous when circles and squares were tracked at the same time, and in Experiment 3 the left- and right-hand motions maintained different frequency ratios. Because haptic tracking has revealed that humans can in fact move their 2 hands independently, it may have potential as a new behavioral tool for revealing other perceptual–motor capabilities. Keywords: touch, movement, coordination, haptics

poral trajectories (Kelso, Southard, & Goodman, 1979; Marteniuk, MacKenzie, & Baba, 1984). A number of models have been developed to explain these movement interactions. The models have ascribed the interactions to neural cross-talk in motor execution (Cattaert, Semjen, & Summers, 1999; Rosenbaum, 1991), to perceptual limitations (Bingham, Zaal, Shull, & Collins, 2001; Mechsner, Kerzel, Knoblich, & Prinz, 2001), to constraints on the regulation of timing (Semjen & Ivry, 2001), to constraints on the regulation of spatial position (Swinnen, Dounskaia, & Duysens, 2002), and to properties of dynamical systems characterizing actor– environment interactions (Schmidt, Carello, & Turvey, 1990; Scho¨ner & Kelso, 1988). To the best of our knowledge, no previous study has shown that people can move their two hands independently for extended periods of time without extensive practice. Research with splitbrain patients has shown that such patients can achieve greater spatial independence between the hands than normal individuals can (Franz, Eliassen, Ivry, & Gazzaniga, 1996), although complete spatial independence between the hands is not evident in these patients. Split-brain patients can achieve greater temporal independence than normal participants can in continuous tasks (Kennerley, Diedrichsen, Hazeltine, Semjen, & Ivry, 2002) but not in discrete positioning tasks (Franz et al., 1996; Preilowksi, 1972; Tuller & Kelso, 1989). Previous studies with normal populations have shown that only after extensive practice with generating polyrhythms some degree of independence is achieved, but even then, the independence that is observed appears for only very brief periods (Krampe, Kliegl, Mayr, Engbert, & Vorberg, 2000; Pressing, Summers, & Magill, 1996; Shaffer, 1984). We sought to create conditions in which bimanual independence could be easily achieved with little or no training. The task we developed was one that enabled participants to move their two hands in a primarily reactive, rather than active, fashion. We called our task haptic tracking. The task entails maintaining gentle contact with a moving object, similar to the touch required for holding the hand of a child while walking, slow dancing with another

Doing two things at once is difficult. It is hard to interpret a stimulus in two different ways at the same time, to think about two unrelated topics simultaneously, or to perform distinct cognitive tasks concurrently. The difficulty of carrying out two tasks at once is not limited to mental performance. It is also manifested in overt movement. As every partygoer knows, it is hard to rub the stomach while patting the head. In laboratory studies of motor interactions, it is difficult to draw different shapes with the two hands at the same time (Franz, Zelaznik, & McCabe, 1991), to wave the two arms at different frequencies (Turvey, 1990; Von Holst, 1973), to generate polyrhythms with the two hands (Klapp, Nelson, & Jagacinski, 1998; Summers, Rosenbaum, Burns, & Ford, 1993), and to aim at targets with the two hands with different spatiotem-

David A. Rosenbaum, Amanda M. Dawson, and John H. Challis, Department of Psychology, Pennsylvania State University. This work was supported by Grant SBR-94-96290 from the National Science Foundation, Grants KO2-MH0097701A1 and R15 NS41887-01 from the National Institute of Mental Health, the Pennsylvania State University Alumni Dissertation Award, and the Research and Graduate Studies Office of the College of Liberal Arts, Pennsylvania State University. Aspects of this study were described in a talk presented at the 43rd Annual Meeting of the Psychonomic Society, Kansas City, Missouri, November 2002; at the 15th Annual Meeting of New England Sequencing and Timing, New Haven, Connecticut, March 2005; at the Workshop on Perception and Action, Giessen, Germany, August 2005; and at the Winer Lectures, Purdue University, October 2005. We thank Jennifer Bittner, Francis Bonadio, Ruben Cancio, Karisa Cortellini, Jessica Erschen, Jackie Graham, Jeremy Graham, Lindsay Hill, Crystal Kane, Kelly Manley, Jack Mutzabaugh, Peter Starr, Laura Tagliareno, and Andrea Weiner for assistance with data collection and analysis, and we thank Jo¨rn Diedrichsen, Liana Brown, Rajal Cohen, Glyn Humphreys, Richard Jagacinski, Steven Jax, Judith Kroll, and Mark Latash for helpful comments. Correspondence concerning this article should be addressed to David A. Rosenbaum, 642 Moore Building, Department of Psychology, Pennsylvania State University, University Park, PA 16802. E-mail: [email protected] 1266

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person, or staying in light contact with one’s aikido partner. Our question was whether people can perform haptic tracking with two hands at once. We were especially interested in the possibility that during haptic tracking people could carry out hand movements that are independent or otherwise difficult to perform concurrently. We thought bimanual decoupling might be possible during haptic tracking because prior studies have shown that haptically driven responses are natural and automatic. Manual grip forces are adjusted quickly in response to slip (Johannson & Westling, 1988), light touch with the hand on a stable surface reduces postural sway (Jeka & Lackner, 1994), and choice reaction times to vibrotactile stimuli are so short that they hardly increase with the number of stimulus–response alternatives (Leonard, 1959). Such outcomes may be due, at least in part, to direct ipsilateral connections across the central sulcus between primary somatosensory cortex and primary motor cortex (Kelly & Dodd, 1991). Haptic pursuit tracking constitutes a poorly understood, and as yet understudied, area of perceptual–motor control. We chose to study it with two hands because we thought the most dramatic finding we could obtain is that haptic tracking allows for bimanual independence. Were we to obtain this outcome, the result would not only show that haptic tracking is easy. It would also show, for the first time, that neurologically normal, untrained individuals can easily move their two hands in a fully decoupled fashion. This finding would constrain existing models of bimanual coordination.

Experiment 1 In the first experiment participants pressed the tips of their two middle fingers against two buttons, mounted beneath two vertical shafts whose positions were moved rapidly and quasi-randomly in the horizontal plane. In one condition, the two shafts were displaced by one human driver, whereas in the other condition the shafts were displaced by two human drivers (Figure 1). The participants’ task was to keep the tips of both middle fingers in contact with the buttons for as long as possible in each trial while keeping their eyes closed. We expected the shafts to be moved in a correlated fashion when displaced by one driver and to be moved in an uncorrelated fashion when displaced by two drivers. We hypothesized that if these expectations were met and if the motions of the shafts were otherwise comparable, participants would be able to haptically pursue the shafts equally well in the one- and two-driver conditions.

Method Participants. The participants were 16 healthy, right-handed Penn State University undergraduates. All were tested according to the ethical guidelines of the American Psychological Association and with the approval of the Penn State University Institutional Review Board. Procedure, design, and apparatus. The experimenters who drove the shafts were two young women (Penn State undergraduates) of approximately equal height and weight. Each participant was tested in the one- and two-driver conditions in alternation in all possible orders across participants, and with the left–right positions of the experimenters in the twodriver condition balanced across participants. Each condition was tested in four consecutive trials. Throughout each trial, the participant and driver(s) sat facing each other. Each trial began with the experimenter(s) holding the shafts about 40 cm in front of their own and the participant’s torsos. Participants used visual guidance to bring

1267 1 Driver

P

2 Drivers

P

Figure 1. Experimental conditions experienced by the participant (P) in the one-driver (top panel) and two-driver (bottom panel) bimanual haptic pursuit tasks of Experiment 1.

their hands to the start positions and then closed their eyes. Participants were unaware whether one or two drivers were going to operate the paddles in any given trial. Once the buttons were pressed, the experimenter(s) checked that the participant’s eyes were closed and began moving the shafts as quickly as possible, attempting to displace the shafts in random directions and over random distances, subject to the constraints that the manipulanda did not collide, that the shafts remained vertically oriented, that the bases of the manipulanda remained at a height corresponding to the middle of the torso, and that both buttons remained in reach by the participant. The shafts were made of wood, were 19.69 cm long and 2.38 cm in diameter, and weighed 878.85 g. On top of each shaft were two infraredemitting diodes (IREDs) whose positions were recorded with an OPTOTRAK motion tracking system (Northern Digital Corp., Waterloo, Ontario, Canada) sampling at 100 Hz. One IRED on each shaft was illuminated throughout the trial. The other IRED was illuminated only when the button beneath it was pressed. The shaft was mounted at the center of a wide circular base that was wide enough (31 cm in diameter) to prevent participants from grabbing hold of the disk when pressing the button. Together, the base and shaft resembled an air hockey paddle. The button had a brass surface that was 2.38 cm in diameter, flush with the bottom surface of the circular base when it was closed, and protruded only 0.16 cm when open. Closing the button’s switch required 1.75 N of force (0.393 lb). The separation between the lateral edge of the button and the inner wall of the wooden disk was so small (0.32 cm) that participants could not press sideways on the button. The OPTOTRAK began storing the shaft positions when both buttons were closed and continued to do so for 20 s. When the data recording was complete, the participant and experimenter(s) rested.

Results and Discussion As shown in Figure 2A, instantaneous directions of motion in the horizontal plane were correlated in the one-driver condition but were uncorrelated in the two-driver condition. Similarly, as shown

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Figure 2. Bimanual haptic tracking data from the one- and two-driver conditions of Experiment 1. (A) Correlations between instantaneous directions of left- and right-shaft motions. (B) Correlations between instantaneous left- and right-shaft tangential velocities. (C) Mean tangential velocities. (D) Proportion of trial time during which bimanual contact was maintained prior to first loss of contact. Correlations in Panel A were computed using circular statistics, a method that prevents spurious numerical jumps associated with discontinuities around 2␲ radians and integral multiples thereof (Fisher, 1993).

in Figure 2B, instantaneous tangential velocities of the left and right shafts were correlated in the one-driver condition but were uncorrelated in the two-driver condition. Finally, as shown in Figure 2C, mean tangential velocities of the shafts in the horizontal plane were statistically indistinguishable in the one- and twodriver conditions. The foregoing results concerned what the drivers did. The remaining data concern what the participants did. Their data appear in Figure 2D, where it is seen that there was no difference between the proportions of time within the 20-s trials when participants lost contact with at least one button. The proportions were low, confirming our expectation that this would be an easy task.

Experiment 2 Although the results of the first experiment were promising, we had four concerns about them. First, we were concerned that participants’ hands may have been passively dragged by the manipulanda. Second, the measures we took may have failed to pick up subtle differences between the patterns of motions of the two target shafts in the one- and two-driver conditions. Thus, even though the correlations between the motions of the two moving targets were significantly different from zero for the one-driver condition and not significantly different from zero for the two-

driver condition for the variables we considered (instantaneous directions of motion and instantaneous speeds), it is possible that the motions were actually correlated in the two-driver condition for other variables, the number of which is potentially limitless. Third, the measure of the participants’ tracking performance was coarse. Because participants could press anywhere on the surface of the button, they could have closed the circuit and illuminated the IRED over a wide range of positions. Fourth and finally, the trials were short, only 20 s. To address these concerns, we redesigned the apparatus and method in several ways. First, we used four conditions, all of which had two drivers. In one condition both drivers generated squares, in a second condition both drivers generated circles, in a third condition the driver on the left generated a square while the driver on the right generated a circle, and in the fourth condition the driver on the left generated a circle while the driver on the right generated a square. We were especially interested in the simultaneous tracking of the circle and square, because it is difficult to generate curved lines and straight lines simultaneously (Franz et al., 1991). It is also difficult to keep one hand moving while the other hand stops (e.g., Franz et al., 1996). The second change we made was to eliminate the possibility that passive drag could account for successful tracking. We did this by

BIMANUAL HAPTIC TRACKING

designing an apparatus whose most important property was that participants could not push on the tracked object with enough force to be passively dragged by it. Details about the apparatus are given in the Method section. The third change allowed for a more sensitive measure of performance than was possible before. Rather than record the buttons’ switch closings and openings, as in the first experiment, in the second experiment we measured the correspondence between the positions of the to-be-tracked stimuli and the participant’s hands. This allowed us to see how well participants could track the shapes when the shapes were different or the same and to see how well participants could track with one hand when the other hand’s trajectory had well-defined characteristics. For example, we could evaluate how well participants tracked a circle with one hand while tracking a square with the other. Fourth and finally, the duration of observation was extended from 20 s per condition to 2 min per condition.

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driving positions (left vs. right), as well as the set of templates within which the paddles moved. The inner edge of the templates was either a circle (diameter ⫽ 46 cm) or a square (edge length ⫽ 46 cm). Because the paddle radius was 15.5 cm, the diameter of the circle described by the moving target was 46 cm – (2 ⫻ 15.5 cm) ⫽ 15 cm. Similarly, the length of each side of the square described by the moving target was 15 cm. The templates were cut into a square of corrugated plastic (edge length ⫽ 55 cm) that could be easily attached to and removed from the glass with large clamps. Each driver could move in a square template or a circular template. The necessary template was clipped to the glass as needed depending on

Method Participants. Ten healthy, right-handed undergraduates at Penn State University participated. Procedure, design, and apparatus. To accommodate the physical requirements of the new apparatus, the plane of paddle motion was rotated from the horizontal plane to the vertical plane, and participants and experimenters stood upright (Figure 3). The experimenters and participant were separated by an opaque pane of glass (76 cm ⫻ 92 cm ⫻ 3 mm). Each experimenter moved a paddle on his or her side of the glass, resulting in the movement of a 5.08-cm-diameter plastic disk (a target button) on the other side of the glass, which was haptically tracked by the participant with one of his or her hands. To couple each target button to its respective paddle, we used a pair of rare-earth magnets (Grade 40 neodymium; National Imports LLC, Fall Church, VA) that attracted each other through the glass. The magnets decoupled when a force greater than 0.3760 N (0.0845 lb) was applied to the target button. This is a very small force, what one participant called “feather light.” Of most importance, the forces that could be applied to the target button and still allow the target button to remain coupled to the driving paddle were insufficient to drag the arm. This statement is based on the fact that the human arm has a mass of approximately 5% of a human adult’s total body mass (Dempster, 1955), causing the arm of a 150-lb adult to have a mass of 7.5 lb. This value is much greater than the 0.0845 lb that would have caused decoupling of the magnets. The target buttons were made of highly polished polymer, providing a slick, low-friction surface, which discouraged participants from establishing a firm finger grip. Seven thin plastic strips were glued to the surface of the target buttons so they radiated from the center of the buttons in a pie-wedge formation (see Figure 3). Participants were instructed to keep the tip of the middle finger as close as possible to the point where the rays converged. IREDs were affixed to the participant’s middle and ring fingers of both hands, allowing for measurement of the participant’s finger positions. To record the positions of the drivers’ paddles, IREDs were affixed to the ends of “antennas” that extended from each paddle up by 62 cm and then down by 52 cm over the top of the glass. The antennas enabled the OPTOTRAK to record the paddle positions as well as the participants’ finger positions. By knowing the positions of the paddle antennas, it was possible to determine where the paddles were relative to the participant’s fingers. Four young women (three Penn State undergraduates and one graduate student, Amanda M. Dawson), who were of approximately equal height and weight, alternated responsibility for driving the paddles, monitoring participants’ performance, and controlling the OPTOTRAK. Between trials, the two experimenters who drove the paddles switched their own

Figure 3. Setup for Experiment 2. Top panel: Two drivers moving paddles in a square template (left) and in a circular template (right). Middle panel: A participant haptically tracking the two magnetically driven target buttons. Bottom panel: Target button and participant’s index finger without infrared-emitting diodes attached.

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the condition being tested. The four conditions were administered in a random order across participants. Participants agreed to be blindfolded and to listen to white noise over headphones during the practice and experimental trials. The experimenters could not see participants through the opaque glass. For 2 min prior to the beginning of the first trial, participants were allowed to practice haptically tracking the target buttons as the buttons were moved randomly on the surface of the glass. Then the drivers attached the templates to the glass and brought the paddles into their “home” positions—at 2 o’clock for the left-hand shape and at 10 o’clock for the right-hand shape from the participant’s perspective. The motions of the paddles were mirrorsymmetrical about the vertical axis. The driver on the left moved clockwise while the driver on the right moved counterclockwise. The drivers were instructed to align the paddles with marks at each of the four corners of the square template in time with successive clicks of a metronome sounding every 0.5 s. Likewise, the drivers were instructed to align the paddles with “corner” marks at 45°, 135°, 225°, and 315° along the rim of the circle template in time with the same metronome. They were told not to pause the paddles at these corner positions while generating circles. The drivers listened to the metronome over headphones. The participant could not hear the metronome. We anticipated that participants might lose contact with a button or press hard enough on a button to decouple it from its paddle. Accordingly, we ran the experiment in such a way that if either type of error occurred, the trial was stopped and then started again with both paddles at their home positions. All the time spent in a condition was accumulated until the participant completed 2 min of haptic tracking in that condition. The number of trials that a participant needed to complete 2 full minutes of haptic tracking within a condition provided a measure of how hard or easy that condition was. At the end of the experiment, participants were debriefed.

Results and Discussion As in Experiment 1, we first evaluated the target motions and then analyzed how well participants tracked the target motions. Target motions. IRED position data from the drivers’ paddles were compared with perfectly formed circles and squares (generated from their respective equations). The analysis confirmed that the experimenters generated the necessary shapes correctly. When circles were to be drawn, the mean coefficient of determination between the paddle positions and an ideal circle (r2) was .9979. When squares were to be drawn, the mean coefficient of determination between the paddle’s positions and an ideal square was .9976. There was no indication that the quality of fit for a circle or for a square was affected by the side on which the shape was traced, by the identity of the experimenter, by the identity of the participant, or by whether the other shape matched or mismatched. To evaluate the timing of the target motions, we conducted two analyses. The first was concerned with the synchrony of movements on the left and right. Using a repeated measures analysis of variance, we compared the difference between the mean times taken for the left and right paddles to reach their corner positions. Table 1 shows the relatively small mean differences between these arrival times. The overall time difference was only 2.93 ms (SE ⫽ 0.25 ms). There was no change in left–right asynchrony depending on whether the left and right target motions followed the same shape or different shapes, F(1, 9) ⫽ 4.939, p ⬎ .05. The second analysis of the timing of target motions was concerned with the extent to which the delays between successive arrivals of the targets at their corner positions corresponded to the ideal delay of 500 ms (determined by the timing set by the

Table 1 Experiment 2: Means (and Standard Errors) of the Time Differences (ms) Between the Left and Right Paddles to Reach the “Corners” of Their Respective Shape Templates Right paddle Left paddle

Circle

Square

Circle Square M

3.02 (0.16) 2.78 (0.31) 2.90 (0.24)

2.96 (0.27) 2.97 (0.24) 2.96 (0.26)

metronome). As shown in Table 2, experimenters were able to keep up with the metronome, on average departing from the ideal delay by only 8.40 ms (SE ⫽ 17.86 ms). The departures from the ideal delay were statistically indistinguishable from zero and did not depend on whether the experimenters generated the same or different shapes, F(1, 9) ⫽ 4.129, p ⬎ .05. Tracking performance. We next addressed the main question of interest: How well did participants haptically track the targets? The analyses reported below bear out what was obvious from watching participants and from hearing their reports—namely, that the participants performed the task very easily and found the task was simple, no matter what condition was tested. To provide a more formal, detailed account of participants’ tracking performance, we conducted several analyses. The first concerned the number of trials participants needed to complete 2 min of tracking in each condition. The relevant data are shown in Table 3, where it is seen that the mean number of trials required to complete a condition was low, with most participants requiring just one or, at most, two trials. The number of necessary trials did not vary with condition. A repeated measures analysis of variance indicated that the number of trials needed to complete 2 min of tracking was not significantly influenced by the shapes being tracked or by whether the shapes were the same or different ( ps ⬎ .05). The next analysis concerned participants’ ability to track the positions of the paddles. To evaluate participants’ tracking abilities, we computed a measure of the difference between the instantaneous displacement of each paddle’s IRED and the instantaneous displacement of the corresponding middle finger IRED (see Figure 4). The measure was the euclidean distance between the endpoints of the paddle displacements and the endpoints of the corresponding hand displacements after the start positions of both displacements were functionally (mathematically) aligned. This measure could take on a value of zero if tracking were perfect and could grow as the target and hand displacements diverged. The results appear in Table 4, where it is seen that although tracking error was larger when squares were tracked than when circles were tracked, F(1, 9) ⫽ 86.394, p ⬍ .05, tracking error was statistically indistinguishable when participants tracked the same or different shapes, F(1, 9) ⫽ 0.206, p ⬎ .05. No other main effects or interactions were statistically significant in this analysis (all ps ⬎ .05). To provide a more fine-grained analysis of tracking error, we also looked at performance at the corners. The question was whether, when traversing the corners of a square, the other hand would show disruption while making a circle. We used the kine-

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Table 2 Experiment 2: Means (and Standard Errors) of the Time (ms) for Each Paddle to Reach the “Corners” of the Shape Templates Other hand’s shape One hand’s identity and shape Left Circle Square Right Circle Square M

Same

Different

487 (22) 521 (21)

502 (13) 520 (17)

505 (28) 505 (7) 504 (20)

522 (26) 506 (8) 512 (16)

Note. The ideal, metronome-specified time was 500 ms.

matic data to identify the moments when the square corners were turned, focusing on the 100 ms before through the 100 ms after these critical events. Table 5 shows the tracking error data for these time intervals. The critical comparison was for tracking a circle with one hand while tracking either a circle or a square with the other hand. When the left hand tracked a circle, its tracking error was only 0.09 mm larger when the right hand tracked a square than when the right hand tracked a circle, and when the right hand tracked a circle, its tracking error was only 0.40 mm smaller when the left hand tracked a square than when the left hand tracked a circle. Neither difference was significant. An analysis of variance confirmed that it did not matter whether the left and right hands tracked the same shape or different shapes ( p ⬎ .05). This outcome was further corroborated in an analysis of tracking in the “straight-aways” (i.e., performance in the 100 ms before through the 100 ms after passing through the midpoints between the corners). As seen in Table 6, tracking errors were again statistically indistinguishable if the two hands tracked shapes that were the same or different ( p ⬎ .05). The last aspect of the results concerns participants’ comments about the task. As mentioned above, participants said they found the task very easy. Another point that bears on the interpretation of participants’ cognitive states while doing haptic tracking is that without exception, participants reported that they were aware that they were making circles and squares. Participants were able to report this even though they never saw the templates and were never told that circles or squares were part of the experiment. Participants were also asked whether some trials seemed more difficult than others. Most participants said they found it harder to Table 3 Experiment 2: Means (and Standard Errors) of Number of Attempts Needed to Complete 2 Min of Haptic Tracking in Each Combination of Shapes Right shape Left shape

Circle

Square

Circle Square

1.30 (0.95) 1.10 (0.32)

1.10 (0.32) 1.60 (1.90)

Note.

Perfect performance is one attempt.

Figure 4. Target displacements (solid arrows), hand displacements (dashed arrows), and euclidean distance between the two (heavy lines) in single OPTOTRAK frames. Tracking error is largest in the left panel and smallest in the right panel. Data are only hypothetical, for didactic purposes.

track squares than circles, but none reported that it was harder to track squares and circles at the same time than to track two circles or two squares at the same time. Participants expressed surprise that they were able to make a circle and a square simultaneously in this context.

Experiment 3 The comments of the participants in Experiment 2 raise the concern that, because they were aware that they were tracking circular and square motions, their success in the tasks may have relied on strategic attention allocation (see Franz, 2004). In particular, they may have paid special attention to the squares’ corners when they made circular arcs with the other hand. If this strategy were used, it would not vitiate the main finding of bimanual independence, but it would raise questions about the need for special attentional strategies at critical points in those conditions. To address this concern and to further evaluate the generality of the capacity for bimanual independence in haptic tracking, we exploited one of the most robust phenomena in the study of bimanual performance—the tendency of the two hands to veer toward simple frequency ratios when both hands generate cyclic movements. The simplest frequency ratio, and the one toward which the hands gravitate the most as driving frequencies increase, is 1:1. A frequency ratio that is very hard to maintain, except at Table 4 Experiment 2: Means (and Standard Errors) of Euclidean Distances (mm) Between Endpoints of Paddle Displacements and Endpoints of Corresponding Hand Displacements Other hand’s shape One hand’s identity and shape Left Circle Square Right Circle Square M

Same

Different

1.22 (0.41) 1.25 (0.30)

1.21 (0.22) 1.05 (0.37)

1.86 (0.51) 1.82 (0.53) 1.54 (0.44)

1.88 (0.47) 1.92 (0.47) 1.51 (0.38)

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Table 5 Experiment 2: Means (and Standard Errors) of Euclidean Distances (mm) Between Endpoints of Paddle Displacements and Endpoints of Corresponding Hand Displacements at “Corners” Other hand’s shape One hand’s identity and shape Left Circle Square Right Circle Square M

Same

Different

1.23 (0.50) 1.18 (0.54)

1.32 (0.52) 1.14 (0.43)

1.97 (1.44) 2.13 (1.17) 1.63 (0.91)

1.57 (0.42) 1.97 (1.17) 1.50 (0.64)

very low driving frequencies or with extensive practice, is 3:4 (3 cycles of the left hand for every 4 of the right) or 4:3 (4 cycles of the left hand for every 3 of the right; Peper, Beek, & van Wierengen, 1995; Zanone & Kelso, 1997). In Experiment 3, we asked whether 3:4 and 4:3 frequency ratios are harder to produce than 1:1 frequency ratios in haptic tracking. We asked participants in the third experiment to make circular haptic-tracking movements with the two hands simultaneously such that the left hand moved at 0.500 Hz or 0.375 Hz and the right hand moved at 0.500 Hz or 0.375 Hz. Pairing the left- and right-hand frequencies in all four possible ways led to frequency ratios of 1:1 (0.375 Hz paired with 0.375 Hz or 0.500 Hz paired with 0.500 Hz), 3:4 (left 0.375 Hz paired with right 0.500 Hz), and 4:3 (left 0.500 Hz paired with right 0.375 Hz). An important feature of the resulting motion patterns was that the phase lags of the two hands changed continuously in the 3:4 and 4:3 frequency ratios. Thus, for these ratios, and also for the 1:1 frequency ratios, there was no critical point in the circular motions when it would have been a priori especially advantageous for participants to attend to one hand rather than another. Consequently, if strategic attention allocation to critical points was responsible for bimanual independence in Experiment 2, one would expect performance to suffer in the complex frequency ratios (3:4 and 4:3) as compared with the simple frequency ratio (1:1). By contrast, if bimanual independence in Experiment 2 reflected some inherently easy Table 6 Experiment 2: Means (and Standard Errors) of Euclidean Distances (mm) Between Endpoints of Paddle Displacements and Endpoints of Corresponding Hand Displacements in the “Straight-Aways”

feature of haptic tracking, one would expect participants to do just as well at bimanual haptic tracking with complex frequency ratios as with simple frequency ratios.

Method Participants. Twelve healthy, right-handed undergraduates at Penn State University participated. Procedure, design, and apparatus. The apparatus originally designed for Experiment 2 was used in Experiment 3. IREDs were used to record the positions of the driver paddles and the middle and ring fingers of the participants. Participants attempted to keep the tips of their fingers as close as possible to the middle of the tracked stimuli. Participants performed the tasks blindfolded and while listening to white noise over headphones, as before. Four young women and one young man (four Penn State undergraduates and one graduate student, Amanda M. Dawson), of approximately equal height and weight, alternated as paddle drivers, performance monitors, and computer operators. Each driver used a circular template and placed his or her paddle into the beginning “home” positions, which were identical to those used in Experiment 2, namely, at 2 o’clock for the left-hand shape and 10 o’clock for the right-hand shape, from the participant’s perspective. Participants tracked clockwise motions with the left hand and counterclockwise motions with the right hand. Each of the four frequency conditions was administered twice in two separate blocks and in a randomized order across participants. Successful completion of a condition required 1 full minute of accurate haptic tracking. (We reduced the time from 2 min in Experiment 2 to reduce fatigue and to provide multiple trials in any one condition. Total time spent in a condition across the two blocks was still 2 min.) Time spent in a condition was accumulated across multiple trials if a condition’s trial had to be discontinued because of an error (i.e., the participant lost contact with the target or decoupled the magnets between the target button and paddle).

Results and Discussion Target motions. The first analysis concerned the target motions generated by the human drivers. We measured the cycle completion times on the basis of successive times of arrival of the paddles at the corner positions on the circumference of the left and right circles, as in Experiment 2. As shown in Table 7, the times to complete the revolutions were close to the required periods of 2,000 ms when the target frequency was 0.500 Hz, although the left-circle periods were somewhat shorter on average than the right-circle periods. The times to complete revolutions were also close to the required period of 2,670 ms when the target frequency was 0.375 Hz, although cycle times were generally shorter than the Table 7 Experiment 3: Means (and Standard Errors) of Obtained Periods (ms) When the Target Periods Were 2,000 ms (0.500 Hz) and 2,670 ms (0.375 Hz)

Other hand’s shape Other hand’s target period One hand’s identity and shape Left Circle Square Right Circle Square M

Same

Different

1.21 (0.51) 1.39 (0.53)

1.09 (0.25) 1.23 (0.21)

1.23 (0.21) 2.64 (0.91) 1.62 (0.54)

2.23 (0.56) 2.59 (1.33) 1.79 (0.59)

One hand’s identity and target period (ms) Left 2,000 2,670 Right 2,000 2,670

Same

Different

2,007 (22) 2,607 (8)

2,006 (7) 2,602 (11)

1,958 (15) 2,599 (11)

1,954 (15) 2,585 (11)

BIMANUAL HAPTIC TRACKING

required periods in this condition and again tended to be shorter for the left circle than for the right. The generated periods were significantly different when the target periods were 2,000 ms versus 2,670 ms for a given hand, F(1, 12) ⫽ 8,903.78, p ⬍ .01, but the period generated for a given hand was not statistically affected by the other hand’s required period. From the mean obtained periods of each hand, we calculated the mean obtained frequency ratios in the four conditions of the experiment. These were 1.025 when both hands’ target period was 2,000 ms (0.500 Hz), 1.003 when both hands’ target period was 2,670 ms (0.375 Hz), 0.776 when the target periods were 2,000 ms (0.500 Hz) for the left hand and 2,670 ms (0.375 Hz) for the right, and 1.331 when the target periods were 2,670 ms (0.375 Hz) for the left hand and 2,000 ms (0.500 Hz) for the right. These values are close to the ideal values of 1.000, 1.000, 0.750, and 1.333. Tracking performance. We next evaluated participants’ haptic tracking performance. In the first analysis we tallied the number of trials participants required to complete 1 full minute of any given condition, with one trial being the minimum required and a larger number of trials corresponding to greater difficulty. The number of trials required to complete a condition was low, with most participants needing only one trial. Although, as shown in Table 8, there was a tendency for more trials to be needed when the target periods mismatched than when they matched, the interaction between target period and match or mismatch of target period was not statistically significant ( p ⬎ .05). To get a more fine-grained picture of performance in the four conditions of the experiment, we analyzed the mean euclidean distance between vector endpoints of the paddle and corresponding hand, as in Experiment 2. The results appear in Table 9. Quality of tracking performance, as revealed by displacement errors, was very good. The displacement errors were very small, and there was no main effect of whether the two hands’ frequencies matched or mismatched, F(1, 12) ⫽ 0.283, p ⬎ .05. No other main effect or interaction approached statistical significance.

General Discussion In this study we tested the hypothesis that haptic tracking might provide a special context in which neurologically normal human adults could move their hands independently for extended periods of time with little or no practice. Our results confirmed this hypothesis. In Experiment 1 participants haptically tracked two horizontally moving objects that were driven either in a correlated fashion by one human driver or in an uncorrelated fashion by two human

Table 8 Experiment 3: Means (and Standard Errors) of Number of Attempts Needed to Complete 1 Min of Haptic Tracking in Each Combination of Frequencies Right target period (ms) Left target period (ms)

2,000

2,670

2,000 2,670

1.21 (0.12) 1.36 (0.15)

1.29 (0.14) 1.07 (0.07)

Note.

Perfect performance is one attempt.

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Table 9 Experiment 3: Means (and Standard Errors) of Euclidean Distances (mm) Between Endpoints of Paddle Displacements and Endpoints of Corresponding Hand Displacements Other hand’s target period One hand’s identity and target period (ms) Left 2,000 2,670 Right 2,000 2,670 M

Same

Different

2.56 (0.90) 2.03 (0.78)

1.65 (0.68) 1.46 (0.29)

1.99 (0.50) 1.56 (0.58) 2.04 (0.69)

1.86 (0.53) 2.51 (0.72) 1.87 (0.55)

drivers. Our participants tracked the two objects equally well in these two conditions. In Experiment 2 participants haptically tracked two vertically moving objects that followed circular or square patterns. The participants tracked the two patterns equally well regardless of whether the patterns were the same (two circles or two squares) or different (a circle and a square). The apparatus in Experiment 2 made it impossible for participants’ arms to be passively dragged by the moving objects. Because participants in Experiment 2 could haptically track as well as they did with no possibility of being passively dragged, their fine performance argues against the possibility that participants in Experiment 1 did as well as they did because their hands were passively dragged. In Experiment 3 we further checked the capacity for bimanual independence in haptic tracking by exploiting one of the most robust phenomena of bimanual movement generation—the tendency of the two hands to be drawn toward simple frequency ratios such as 1:1 when the task requires a more complex frequency ratio such as 3:4 or 4:3. When participants in Experiment 3 haptically tracked circular motions with 3:4 or 4:3 frequency ratios, they did just as well as when they haptically tracked circular motions with 1:1 frequency ratios. Owing to the novelty of our methods (but see Burke, Gilson, & Jagacinski, 1980; Navas, 1964), we need to be as clear as possible about what we are and are not claiming. We are making two claims. One is that bimanual independence is easily achieved with haptic tracking. The other is that bimanual coupling, when it has been observed in previous studies that required arm movements similar to ours, cannot be ascribed to interactions at the level of movement execution per se (e.g., interactions at the level of the spinal cord), contrary to the suggestion made by some that this may have been the case (Cattaert et al., 1999; Rosenbaum, 1991). Our experiments indicate that people are physically capable of moving their two hands independently. What we are not claiming is that our results rule out dynamical systems accounts of bimanual interactions. Such accounts have been developed in considerable detail, have motivated many important studies, and have contributed much to our understanding of the quantitative regularities of interlimb interactions (e.g., Kelso, 1996; Ridderikhoff, Peper, & Beek, 2005). The data presented here can be modeled with dynamical systems equations—for example, by setting coupling strength to zero, by modifying coupling strength with additional terms (cf. Amazeen, Amazeen, Treffner,

ROSENBAUM, DAWSON, AND CHALLIS

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& Turvey, 1997), or by appreciating that there can be coupling to external events (Jirsa, Fink, Foo, & Kelso, 2000). The fact that bimanual coupling has been a mainstay of research in the dynamical systems framework does not mean that that framework is undermined by our discovery of conditions in which bimanual coupling is less obligatory than was previously believed. How do we interpret our finding that bimanual independence is possible in haptic tracking but is basically impossible in more conventional two-hand movement tasks? We propose that our results point to high-level control as the locus of bimanual coupling in more conventional two-hand movement tasks. We base this proposal on the idea that haptic tracking obviates high-level planning of large-scale movement paths. This interpretation fits with the fact that our participants exhibited bimanual independence with essentially no practice when they engaged in haptic tracking, which contrasts with the fact, mentioned earlier, that in the case of generating polyrhythms, only a modicum of independence is achieved between the hands in neurologically normal individuals and only for very brief periods and only in people who are very highly practiced (Krampe et al., 2000; Pressing et al., 1996; Shaffer, 1984). Our proposal that haptic tracking obviates high-level planning of large-scale movement paths also agrees with other emerging views of bimanual coupling as being mainly due to cognitive factors (Diedrichsen, Hazeltine, Kennerley, & Ivry, 2001; Franz, Zelaznik, Swinnen, & Walter, 2001; Kunde & Weigelt, 2005; Mechsner et al., 2001). More research will be needed to test this idea further and to shed light on the mechanisms underlying haptic tracking.

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Received June 13, 2005 Revision received May 10, 2006 Accepted May 18, 2006 䡲